Global navigation satellite systems include Global Positioning System (GPS) (United States), GLONASS (Russia), Galileo (Europe), and COMPASS (China) (systems in use or in development). A GNSS typically uses a plurality of satellites orbiting the earth. The plurality of satellites forms a constellation of satellites. A GNSS receiver detects a code modulated on an electromagnetic signal broadcasted by a satellite. The code is also called a ranging code. Code detection includes comparing the bit sequence modulated on the broadcasted signal with a receiver-side version of the code to be detected. Based on the detection of the time of arrival of the code for each of a series of the satellites, the GNSS receiver estimates its position. Positioning includes, but is not limited to, geolocation, i.e. the positioning on the surface of the Earth.
An overview of GPS, GLONASS and Galileo is provided for instance in sections 9, 10 and 11 of Hofmann-Wellenhof B., et al., GNSS, Global Navigation Satellite Systems, GPS, GLONASS, Galileo, & more, Springer-Verlag, Vienna, Austria, 2008, (hereinafter referred to as “[1]”), which is hereby incorporated by reference in its entirety.
Positioning using GNSS signal codes provides a limited accuracy, notably due to the distortion the code is subject to upon transmission through the atmosphere. For instance, the GPS includes the transmission of a coarse/acquisition (C/A) code at 1575.45 MHz, the so-called L1 frequency. This code is freely available to the public, in comparison to the Precise (P) code, which is reserved for military applications. The accuracy of code-based positioning using the GPS C/A code is approximately 15 meters, when taking into account both the electronic uncertainty associated with the detection of the C/A code (electronic detection of the time of arrival of the pseudorandom code) and other errors including those caused by ionospheric and tropospheric effects, ephemeris errors, satellite clock errors and multipath propagation.
An alternative to positioning based on the detection of a code is positioning based on carrier phase measurements. In this alternative approach or additional approach (ranging codes and carrier phases can be used together for positioning), the carrier phase of the GNSS signal transmitted from the GNSS satellite is detected, not (or not only) the code modulated on the signal transmitted from the satellite.
The approach based on carrier phase measurements has the potential to provide much greater position precision, i.e. up to centimeter-level or even millimeter-level precision, compared to the code-based approach. The reason may be intuitively understood as follows. The code, such as the GPS C/A code on the L1 band, is much longer than one cycle of the carrier on which the code is modulated. The position resolution may therefore be viewed as greater for carrier phase detection than for code detection.
However, in the process of estimating the position based on carrier phase measurements, the carrier phases are ambiguous by an unknown number of cycles. The phase of a received signal can be determined, but the cycle cannot be directly determined in an unambiguous manner. This is the so-called “integer ambiguity problem”, “integer ambiguity resolution problem” or “phase ambiguity resolution problem”.
GNSS observation equations for code observations and for carrier phase observations are for instance provided in [1], section 5. An introduction to the GNSS integer ambiguity resolution problem is provided in [1], section 7.2.
Patent application US 2005/0264444 A1 relates to a system combining, for determining the position of a receiver, the use of differential carrier-phase measurements with a reference station to perform real-time kinematic (RTK) positioning and the use of a wide-area differential GPS (WADGPS) technique (carrier-phase differential method). The WADGPS includes a network of reference stations in communication with a computational center, or processing hub, to compute error corrections based on the known locations of the reference stations.
According to the teaching in US 2005/0264444 A1, paragraph [0012], “when the communication link for the RTK navigation is available, the position, velocity and time (PVT) outputs of the user receiver can be obtained using the RTK system, while the WADGPS system runs in the background and its outputs are constantly initialized to agree with the outputs from the RTK system. When the communication link for the RTK navigation is lost, or when the user receiver wanders too far away from the reference station in the RTK system, the PVT outputs of the user receiver can be obtained using the WADGPS system, which has been initialized while the RTK was operating”.
There is a need for improving the implementation of positioning systems based on GNSS carrier phase measurements, to obtain a precise estimation of the receiver position in a quick, stable and user-friendly manner.